A Note on High-Dimensional Confidence Regions

Publication date: 19 May 2021

Abstract: Recent advances in statistics introduced versions of the central limit theorem for high-dimensional vectors, allowing for the construction of confidence regions for high-dimensional parameters. In this note,

s

-sparsely convex high-dimensional confidence regions are compared with respect to their volume. Specific confidence regions which are based on

e l l_{p}

-balls are found to have exponentially smaller volume than the corresponding hypercube. The theoretical results are validated by a comprehensive simulation study.

Mathematics Subject Classification ID

Hypothesis testing in multivariate analysis (62H15)

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